Method and system for examining a surface

ABSTRACT

The present invention includes a system and a method of determining the regularity of a surface of an object under examination. The method includes receiving a three-dimensional phase image of the surface including a plurality of pixels, wherein the phase image can result from a multiple wavelength interferometric analysis of the surface. The method can further include the steps of determining a relative height of the pixels in response to the phase image of the surface, creating a statistical map of the surface in response to the relative height of the pixels, and determining the regularity of the surface of the object under examination in response to the statistical map of the surface. The system includes an interferometric apparatus connected to a controller, wherein the controller is adapted to perform one or more functions similar to the method of the present invention.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/827,707 filed 30 Sep. 2006 and entitled “Method and Apparatus forMeasuring Parts”, which is incorporated in its entirety by thisreference.

TECHNICAL FIELD

The present invention relates generally to the field of interferometry,and more particularly to the field of interferometric methods andsystems for determining the regularity of a surface related to amanufacturing process.

BACKGROUND

A large number of manufacturers in the automotive, aerospace,semiconductor, and medical device industries spend countless resourcesand time not only in the design and manufacture of specialized parts,but also in the inspection and quality control procedures that ensurethe proper operation of the finished product. Many of the currentinspection and quality control protocols involve numerous man-hours, andthe tasks are becoming even more complicated given the decreasing sizeof many consumer goods and their constituent parts.

While some automated inspection systems have been developed to aidcompanies in the manufacturing process, many of these systems lack anumber of desirable features. For instance, inspection systems relyingon optical data in the visible range of the electromagnetic spectrum caneasily fail to detect small variations in the surface of an object.Similarly, to the extent that automated systems may use interferometrictechniques, they typically do not employ a sufficient number ofwavelengths to resolve the various ambiguities that arise in thedetection of very small imperfections on very small surfaces.

Thus, there is a need in the interferometry field to create an improvedmethod and system for examining a surface. This invention provides suchimproved method and system.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a flowchart of a method for examining the surface of an objectunder examination in accordance with a method of the preferredembodiment.

FIG. 2 is a flowchart of a method for examining the surface of an objectunder examination in accordance with one or more variations of themethod of the preferred embodiment.

FIG. 3 is a schematic block diagram of a system for examining thesurface of an object under examination in accordance with a system ofthe preferred embodiment.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The preferred embodiments of the invention include a method ofdetermining the regularity of a surface of an object under examination,and a system for examining a surface. The following description of thepreferred embodiments of the invention is not intended to limit theinvention to these preferred embodiments, but rather to enable anyperson skilled in the art of interferometry to make and use thisinvention.

As shown in FIG. 1, the method of the preferred embodiment includes:receiving a three-dimensional phase image of the surface based on amultiple wavelength interferometric analysis of the surface, wherein thephase image of the surface includes a plurality of pixels S102;determining a relative height of the pixels in response to the phaseimage of the surface S104; creating a statistical map of the surface inresponse to the relative height of the pixels S106; and determining theregularity of the surface of the object under examination in response tothe statistical map of the surface S108.

Step S102 of the method of the preferred embodiment recites receiving athree-dimensional phase image of the surface includes a plurality ofpixels, the phase image resulting from a multiple wavelengthinterferometric analysis of the surface. The phase image can begenerated by an interferometric apparatus, such as the one describedbelow, which can be connected to one or more controllers,microcomputers, processors adapted for data and image processing. Thephase image functions in part to determine a range or depth profile of athree-dimensional image of an object, such as for example a precisionmachined part, semiconductor wafer, or any other object underexamination.

Step S104 of the method of the preferred embodiment recites determininga relative height of each of the pixels in response to the phase imageof the surface. Step S104 functions to extract the necessary phase datafor each of the wavelengths used in the interferogram and to reduce theamount of gross data associated with any single pixel in the phaseimage. For example, if the method utilizes six phases of sixteenwavelengths and between ten and twelve bit numbers per pixel, then therewould be approximately one thousand bits of information per pixel. StepS104 reduces the gross amount of data associated with any one pixel byconverting the raw phase and/or wavelength data into a relative heightparameter. The unused gross data can be eliminated or sequestered forlater use according to one or more variations of the method of thepreferred embodiment.

Step S106 of the method of the preferred embodiment recites creating astatistical map of the surface in response to the relative height ofeach of the pixels. Step S106 functions to analyze the relative heightdata and calculate and/or show the statistical relationship between eachof the pixels by segmenting, grouping, normalizing and/or otherwiseorganizing the plurality of pixels according to the statisticalproperties of their relative heights. The statistical properties can bedetermined according to any suitable mathematical or statisticaloperation, including Gaussian analysis, Markovian analysis, and/orregressive or recursive analysis. In one variation of the preferredembodiment, the method can employ a fast Fourier transform (FFT) in oneor both of steps S102 and S104, the results of which can bestatistically analyzed in step S106 to recognize physical patterns inthe surface of the object. For example, if the secondary peaks of theFFT function are displaced a different distance relative to the mainpeak, or if the side lobes of the FFT function are statisticallydifferent, then the method of the preferred embodiment can conclude thatthere is a consistent pattern on the surface of the object, such as arecurring tool mark on a series of precision machined parts.

Step S108 of the method of the preferred embodiment recites determiningthe regularity of the surface of the object under examination inresponse to the statistical map of the surface. Step S108 allows amanufacturer of the object, such as a precision machinist orsemiconductor fabricator, to assess the viability and/or functionalityof its product. The regularity of the surface can be determined throughnormalization of the surface qualities, through comparative processes,or through statistical operations adapted to compare the statistical mapto certain predetermined threshold parameters for the surface contours.

In a variation of the method of the preferred embodiment, the multiplewavelength interferometric analysis of the surface includes more thantwo wavelengths of light. In interferometry, a two-wavelength analysishas an inherent ambiguity level that is inversely proportional to thewavelength separation. Unfortunately, as one decreases the wavelengthseparation for large range ambiguity, the range (depth) resolution ofthe interferometer is also reduced. This inverted relationship betweenambiguity and resolution can be undesirable in certain applications,such as when the surface of the object under examination is a precisionmachined, in which case both high ambiguity and high resolution arerequired. Accordingly, this variation of the method of the preferredembodiment employs more than two wavelengths of light to preserve therange resolution and reduce ambiguity in the interferometric analysis.As noted above, the method of the preferred embodiment can employ atleast up to sixteen wavelengths of light of six phases in order togenerate a suitable amount of data for each pixel in the phase image.

In another variation of the method of the preferred embodiment, stepS102 can further include, for each of the pixels and for each wavelengthof light, extracting a peak value of a Fourier transform resulting in aphase value for each of the pixels. Because the method of the preferredembodiment can employ more than two wavelengths of light, and at leastup to sixteen wavelengths of light per pixel, this variation of stepS102 can include at least up to sixteen Fourier transforms per pixelgenerating at least up to sixteen phase values per pixel. The peak valuecan be determined using curve-fitting techniques and/or by oversamplingthe Fourier transform in the range domain and selecting the peak valueof the range image.

In another variation of the method of the preferred embodiment, stepS108 can further include the step of comparing the statistical map ofthe surface of the object under examination to a statistical map of acomparable surface of a comparable object. This variation of step S108can include for example retaining, in a memory storage device, a historyof any previous analysis of a comparable surface, such as for example asimilar object to that under examination. In one alternative, thestatistical map of the comparable surface is generated by performing atleast steps S102, S104 and S106 on the comparable surface prior toperforming at least step S108 on the surface of the object underexamination. For example, if one or more objects are arranged on aconveyor, the method according to this variation of the preferredembodiment can generate and retain a statistically averaged map of anyprior-examined surfaces, thereby maintaining a running and constantlyupdated normalized surface profile for two or more in a series ofobjects. In another alternative, the statistical map of the comparablesurface can include an idealized statistical map of the comparablesurface. For example, a user and/or operator can input or upload astatistical map of how an ideal surface would appear to aninterferometer, such as a perfectly smooth and perfectly contouredprecision machined part. Any such idealized statistical map can begenerated using a computer aided drafting software program, or a CNCmachining program thereby allowing direct comparison between the objectunder examination and an ideal image of how the object should appear tothe interferometer.

In another variation of the method of the preferred embodiment, stepS108 can further include the step of identifying one or more marks onthe surface of the object under examination in response to thestatistical map of the surface of the object. In this variation of themethod of the preferred embodiment, the method can be employed torecognize tool or machining marks on a precision machined part orobject, which in turn allows a user and/or operator to track theperformance of its machining apparatus. For example, by identifyingand/or tracking one or more of a series of tool marks, this variation onthe method of the preferred embodiment allows a user and/or operator toassess whether the machining equipment is properly functioning, whetherit is causing undue wear on the manufactured parts, whether it needsrepair, and/or whether it needs computational or manual adjustments.

As shown in FIG. 2, the method of an alternative embodiment of theinvention includes, in response to the step of identifying one or moremarks on the surface of the object under examination and based on thestatistical map of the surface of the object, adjusting aninterferometric system in response to a regular mark identified on thesurface of the object under examination Silo. In this alternative, if amark is determined to be a regular mark, relative to its statisticalproperties for example, then this variation of the method can cause oneor both of an interferometer or a controller to adjust its measurementand/or computational behavior in accordance therewith. For example, if atool mark is identified as a regular tool mark, then the controller canbe adjusted such that it automatically recognizes the mark as such,thereby saving a considerable amount of time and computational power innot having to recalculate a detailed statistical map of the surface ofthe object in that designated area.

Another alternative includes step S112, which recites segmenting thethree-dimensional phase image in response to one or more marksidentified on the surface of the object under examination. The one ormore marks can be regular, i.e. generated by repeated machining ortooling, or irregular or aberrant. In response to the segmentation, themethod can perform step S114, which recites adjusting an analysis of oneor more of the pixels in response to the segment in which each of thepixels is disposed. For example, the method can perform one or more ofthe following adjustments to the analysis: adjusting the density of aset of reference pixels usable in determining the relative height of thepixels, adjusting the exposure time of the interferometric system forone or more segments, or adjusting a focal parameter of theinterferometric system for one or more segments. Each of theseadjustments can be performed by or at one or both of an interferometeror a controller.

In another variation, the method of the preferred embodiment may includethe step of identifying a defect on the surface of the object underexamination in response to the three-dimensional phase image of thesurface. As noted above, the range or depth of a pixel can be determinedas a function of the wavelength and phase of the incident light from amultifrequency interferometer. Any aberrant range or height measurementwithin a pixel can be indicative of a surface defect. Additionally, themethod of the preferred embodiment can employ other parameters, such asphase correlation, depth of modulation, and reflectivity as a functionof wavelength in order to determine more information about a sub-pixelsurface feature. In one alternative to this variation, the step ofidentifying a defect on the surface of the object under examination caninclude the step of identifying a defective pixel within the pixels.Defective pixels can be identified by any number of statistical oranalytical methods. For example, a defective pixel can be identified bya relationship between magnitude-based and normalized synchronizationfunctions, a sub-threshold value within a region of a magnitude-based ornormalized synchronization peak function, a global low value in amagnitude-based or normalized synchronization peak function, or based ona spatial relationship between one bad pixel and its surrounding pixels.For example, if one pixel is surrounded by more than five bad pixels,then that pixel can also be identified as defective. Alternatively, ifmore of a pixels immediate neighbors (for example in a three by threematrix) are defective than not, then the center pixel can also beidentified as bad or defective. In another alternative to the variationof the method of the preferred embodiment, the method can furtherinclude the step of clustering the defective pixels in order todetermine (or at least approximate) a parameter of the defect on thesurface, such as size, shape, volume, and/or location. In someindustries, parts or objects must meet certain defect thresholds priorto introduction into the stream of commerce. As such, this alternativeembodiment of the method functions to aggregate any defects in thesurface of the object into what might be considered to be largerdefects, i.e. larger divots, scrapes, pores or tool markings that renderthe object unfit for sale. On the other hand, if defective pixels aresufficiently spaced apart, then that might tend to indicate that theobject, while not having an ideal surface, nevertheless is suitable forits intended purpose.

As shown in FIG. 3, the system 10 of the preferred embodiment includesan interferometric apparatus 12 adapted to generate a three-dimensionalphase image of a surface of an object under examination and a controller14 connected to the interferometric apparatus 12. In the system 10 ofthe preferred embodiment, the controller 14 is adapted to determine arelative height of each of the pixels in response to the phase image ofthe surface; create a statistical map of the surface in response to therelative height of each of the pixels; and determine the regularity ofthe surface of the object under examination in response to thestatistical map of the surface. In operation, one or more objects 16 a,16 b, 16 c, 16 d can be positioned on a platform 40, for example aconveyor, whereupon the system 10 of the preferred embodiment inspectsat least one surface of one or more of the objects 16 a, 16 b, 16 c, 16d.

The interferometric apparatus 12 of the system 10 of the preferredembodiment functions to generate a three-dimensional phase image of anobject 16 b under examination. In one variation of the preferredembodiment, the interferometric apparatus includes a tunable laser 22.Light from the tunable laser 22 can split into object and referencebeams, 34 and 32, respectively, using a plurality of optical components30 arranged according to the particular imaging requirements of thesystem 10. The object beam 34 reflects from an object 16 b and travelsback into a detector array 20. The reference beam 32 is reflected by areference mirror 24 and travels back into the detector array 20 as well.Light from the two beams interferes, and the interference pattern isrecorded by the detector array 20. The interferometric apparatus 12 canfurther include one or more beam conditioners 26, 28 that are adapted toalter the phase, direction, spot size or intensity of any laser lightfrom the tunable laser 22. Phase shifting can be used to record thecomplex-valued interference image, which can be accomplished by movingthe reference mirror 24 with an actuator (not shown). The phase of theinterference image contains information about the profile (also referredto as range or depth) of the object 16 b being inspected.

The interferometric apparatus 12 of the system 10 can be used to performsingle wavelength interferometry, two wavelength interferometry, ormulti-wavelength (i.e., more than two wavelengths) interferometry fromwhich three-dimensional phase images can be developed and analyzed bythe controller 14. As noted above, two-wavelength interferometry has aninherent ambiguity level that is inversely proportional to thewavelength separation. As one decreases the wavelength separation forlarge range ambiguity, the range (depth) resolution of theinterferometer is also reduced. This inverted relationship betweenambiguity and resolution can be undesirable in certain applications,such as when the surface of the object under examination is a precisionmachined part or a semiconductor wafer, in which case both low ambiguityand high resolution are required. Accordingly, this variation of thesystem 10 of the preferred embodiment employs more than two wavelengthsof light to preserve the range resolution and reduce ambiguity in theinterferometric analysis. As noted above, the system 10 of the preferredembodiment can employ at least up to sixteen wavelengths of light of sixphases in order to generate a suitable amount of data for each pixel inthe phase image.

In another variation of the system 10 of the preferred embodiment, thecontroller 14 can be adapted to extract, for each of the pixels and foreach wavelength of light, a peak value of a Fourier transform resultingin a phase value for each of the pixels. Because the system 10 of thepreferred embodiment can employ more than two wavelengths of light, andat least up to sixteen wavelengths of light per pixel, this variation ofthe system 10 can include at least up to sixteen Fourier transforms perpixel generating at least up to sixteen phase values per pixel. As notedabove, the peak value can be determined using curve-fitting techniquesand/or by oversampling the Fourier transform in the range domain andselecting the peak value of the range image.

In another variation of the system 10 of the preferred embodiment, thecontroller 14 can be further adapted to compare the statistical map ofthe surface of the object under examination to a statistical map of acomparable surface of a comparable object. This adaptation of thecontroller 14 can include for example retaining, in a memory storagedevice, a history of any previous analysis of a comparable surface, suchas for example a similar object to that under examination. In onealternative, the statistical map of the comparable surface is generatedby performing a prior analysis on objects 16 c, 16 d on the comparablesurface prior to performing the same analysis on the surface of theobject 16 b under examination. For example, if one or more objects 16 a,16 b, 16 c, 16 d are arranged on a conveyor 40, the controller 14according to this variation of the preferred embodiment can generate andretain a statistically averaged map of any prior-examined surfaces,thereby maintaining a running and constantly updated normalized surfaceprofile for two or more in a series of objects 16 a, 16 b, 16 c, 16 d.In another alternative, the statistical map of the comparable surfacecan include an idealized statistical map of the comparable surface. Forexample, a user and/or operator can input or upload a statistical map ofhow an ideal surface would appear to an interferometer to the controller14. An ideal surface may be representative of a perfectly smooth andperfectly contoured precision machined part. Any such idealizedstatistical map can be generated using a computer aided draftingsoftware program, or a CNC machining program thereby allowing directcomparison between the object 16 b under examination and an ideal imageof how the object should appear to the interferometric apparatus 12.

In another variation of the system 10 of the preferred embodiment, thecontroller 14 can be further adapted to identify one or more marks onthe surface of the object 16 b under examination in response to thestatistical map of the surface of the object 16 b. In this variation ofthe system 10 of the preferred embodiment, the controller 14 can beadapted to recognize tool or machining marks on a precision machinedpart or object, which in turn allows a user and/or operator to track theperformance of its machining apparatus. For example, by identifyingand/or tracking one or more of a series of tool marks, controller 14 canbe adapted to notify a user and/or operator to assess whether themachining equipment is properly functioning, whether it is causing unduewear on the manufactured parts, whether it needs repair, and/or whetherit needs computational or manual adjustments. Suitable notification fromthe controller 14 can be communicated through visual and/or audiosignals, or a combination thereof, using for example a display and/orspeaker system (not shown).

Alternatively, in response to the step of identifying one or more markson the surface of the object under examination in response to thestatistical map of the surface of the object, the controller 14 can beadapted to adjust the measurement and/or analytic capabilities of thesystem 10. For example, if a tool mark is identified as a regular toolmark, then the controller 14 can be adjusted such that it automaticallyrecognizes the mark as such, thereby saving a considerable amount oftime and computational power in not having to recalculate a detailedstatistical map of the surface of the object in that designated area.

In another alternative to the variation of the system 10 of thepreferred embodiment, the controller 14 can be adapted to segment thethree-dimensional phase image in response to one or more marksidentified on the surface of the object under examination. The one ormore marks can be regular, i.e. generated by repeated machining ortooling, or irregular or aberrant. In response to the segmentation, thecontroller 14 can be further adapted to adjust the operation of thesystem 10 at least with reference to the segment in which each of thepixels is disposed. For example, the controller 14 can adjust at leastthe following parameters: the density of a set of reference pixelsusable in determining the relative height of the pixels, the exposuretime of the interferometric apparatus 12 for one or more segments, or afocal parameter of the interferometric apparatus 12 for one or moresegments.

In another variation of the system 10 of the preferred embodiment, thecontroller 14 can be adapted to identify a defect on the surface of theobject 16 b under examination in response to the three-dimensional phaseimage of the surface. As noted above, the range or depth of a pixel canbe determined as a function of the wavelength and phase of the incidentlight from a multifrequency interferometer. Any aberrant range or heightmeasurement within a pixel can be indicative of a surface defect.Additionally, the controller 12 of the system 10 of the preferredembodiment can employ other parameters, such as phase correlation, depthof modulation, and reflectivity as a function of wavelength in order todetermine more information about a sub-pixel surface feature.

In one alternative to this variation of the system 10 of the preferredembodiment, the controller 12 can be adapted to identify a defect on thesurface of the object under examination by identifying a defective pixelwithin the pixels. As noted above, defective pixels can be identified byany number of statistical or analytical methods. For example, adefective pixel can be identified by a relationship betweenmagnitude-based and normalized synchronization functions, asub-threshold value within a region of a magnitude-based or normalizedsynchronization peak function, a global low value in a magnitude-basedor normalized synchronization peak function, or based on a spatialrelationship between one bad pixel and its surrounding pixels. Forexample, if one pixel is surrounded by more than five bad pixels, thenthat pixel can also be identified as defective. Alternatively, if moreof a pixels immediate neighbors (for example in a three by three matrix)are defective than not, then the center pixel can also be identified asbad or defective.

In another alternative to the variation of the system 10 of thepreferred embodiment, the controller 14 can be further adapted tocluster the defective pixels in order to determine (or at leastapproximate) a size of the defect on the surface. In some industries,parts or objects must meet certain defect thresholds prior tointroduction into the stream of commerce. As such, in this alternativeembodiment of the system 10, the controller 12 functions to aggregateany defects in the surface of the object into what might be consideredto be larger defects, i.e. larger divots, scrapes, pores or toolmarkings that render the object unfit for sale. On the other hand, ifdefective pixels are sufficiently spaced apart, then that might tend toindicate that the object, in spite of any minor defects, is neverthelesssuitable for its intended purpose.

The controller 14 of the system 10 of the preferred embodiment can beintegrated with the interferometric apparatus 12 or connected from aremote location. The controller 14 can be adapted to perform variousfunctions and/or steps, which can be implemented or performed with ageneral purpose processor, a Digital Signal Processor (DSP), anApplication Specific Integrated Circuit (ASIC), a Field ProgrammableGate Array (FPGA) or other programmable logic device, discrete gate ortransistor logic, discrete hardware components, or any combinationdesigned to perform the functions and/or steps described herein. Ageneral-purpose processor may be a microprocessor, but in thealternative, the processor may be any conventional processor,microcontroller, or state machine.

As a person skilled in the art of interferometry will recognize from theprevious detailed description and from the figures and claims,modifications and changes can be made to the preferred embodiment of theinvention without departing from the scope of this invention defined inthe following claims.

1. A method of determining the regularity of a surface of an objectunder examination, the method comprising: a) receiving athree-dimensional phase image of the surface based on a multiplewavelength interferometric analysis of the surface, wherein the phaseimage of the surface includes a plurality of pixels; b) determining arelative height of the pixels in response to the phase image of thesurface; c) creating a statistical map of the surface in response to therelative height of the pixels; and d) determining the regularity of thesurface of the object under examination in response to the statisticalmap of the surface.
 2. The method of claim 1, wherein step (a) furtherincludes, for each of the pixels and for each of the wavelengths in theinterferometric analysis, extracting a peak value of a Fourier transformresulting in a phase value for each of the pixels.
 3. The method ofclaim 1, wherein step (a) further includes, for each of the pixels andfor each of the wavelengths in the interferometric analysis, extractingone or more of the parameters selected from the group consisting ofobject reflectivity, Depth of modulation, and response to illuminationwavelength.
 4. The method of claim 1, wherein step (d) further includescomparing the statistical map of the surface of the object underexamination to a statistical map of a comparable surface of a comparableobject.
 5. The method of claim 4, wherein the statistical map of thecomparable surface is provided by performing steps (a), (b), and (c) onthe comparable surface.
 6. The method of claim 4, wherein thestatistical map of the comparable surface includes an idealizedstatistical map of the comparable surface.
 7. The method of claim 1,wherein step (d) further includes identifying one or more marks on thesurface of the object under examination in response to the statisticalmap of the surface of the object.
 8. The method of claim 7, furthercomprising adjusting an interferometric system in response to a regularmark identified on the surface of the object under examination.
 9. Themethod of claim 7, further comprising: e) segmenting thethree-dimensional phase image in response to one or more irregular marksidentified on the surface of the object under examination.
 10. Themethod of claim 9, further comprising: f) adjusting an analysis of oneor more of the pixels in response to the segment in which each of thepixels is disposed.
 11. The method of claim 10, wherein step (g) furtherincludes performing a step from the group consisting of: adjusting thedensity of a set of reference pixels usable in determining the relativeheight of the pixels, adjusting the exposure time of the interferometricsystem for one or more segments, and adjusting a focal parameter of theinterferometric system for one or more segments.
 12. The method of claim1, wherein step (d) further includes identifying a defect on the surfaceof the object under examination in response to the three-dimensionalphase image of the surface.
 13. The method of claim 12, wherein the stepof identifying a defect on the surface of the object under examinationincludes identifying a defective pixel within the pixels.
 14. The methodof claim 13, further comprising the step of clustering the defectivepixels in order to determine a parameter of the defect on the surfaceselected from the group consisting of size, shape, volume, and location.15. A system for examining a surface comprising: an interferometricapparatus adapted to generate a three-dimensional phase image of asurface of an object under examination; and a controller connected tothe interferometric apparatus, the controller adapted to determine arelative height of each of the pixels in response to the phase image ofthe surface; create a statistical map of the surface in response to therelative height of each of the pixels; and determine the regularity ofthe surface of the object under examination in response to thestatistical map of the surface.
 16. The system of claim 15, wherein theinterferometric apparatus is adapted to generate an interferogram of thesurface using more than two wavelengths of light.
 17. The system ofclaim 15, wherein the controller is further adapted to compare thestatistical map of the surface of the object under examination to astatistical map of a comparable surface of a comparable object.
 18. Thesystem of claim 17, wherein the statistical map of the comparablesurface includes stored data of a previous analysis of the comparablesurface.
 19. The system of claim 17, wherein the statistical map of thecomparable surface includes an idealized statistical map of thecomparable surface.
 20. The system of claim 15, wherein the controlleris further adapted to adjust the operation of the interferometricapparatus in response to the identification of a mark on the surface ofthe object under examination.